It might be to save on the requirement for the two GPUs that would be required for the turn round.
Positioning the extra GPU and the removal may impact the access around the aircraft for the short turn round also.
Keeping the APU running also eliminates the APU failing to start, which is required to start the engines.
If the APU fails to start, you will then have to find a third GPU quickly for engine start-up or you will end up with a delay, which BA does not want.